Algebra, Geometry, and Financial Mathematics Essentials

Posted by on May 25, 2026 in Mathematics | 0 comments

Algebra, Linear Graphs & Simultaneous Equations

1. Solving & Simplifying Equations

Algebraic Expressions

  • Ex 1 (Simplify): 3x – 5y + 2x + 8y = 5x + 3y
  • Ex 2 (Expand & Solve): 3(x-4) = 2x+5 → 3x-12 = 2x+5 → x = 17
  • Tips:
    • Only add/subtract exact like terms (same variables).
    • Expand brackets by multiplying the outside term by everything inside.
    • Move the smaller variable first to keep values positive.

Linear Inequalities

  • Ex 1 (Solve): -3x + 4 ≤ 10 → -3x ≤ 6 → x ≥ -2
  • Tips:
    • Flip the sign (<
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Applied Mathematics and Statistical Methods Solutions

Posted by on May 21, 2026 in Mathematics | 0 comments

1. Partial Differential Equations and Probability

(a) Solve the PDE (D² − 3DDʹ)z = 0

The auxiliary equation is obtained by replacing D with m and Dʹ with 1:

m² − 3m = 0 ⇒ m(m − 3) = 0 ⇒ m = 0, 3

Solution: z = f₁(y) + f₂(y + 3x)

(b) Classify the PDE: 4∂²u/∂x² − 4∂²u/∂x∂t + ∂²u/∂t² = 0

Comparing with A·u_xx + B·u_xt + C·u_tt = 0: A = 4, B = −4, C = 1

Discriminant = B² − 4AC = 16 − 16 = 0

Since B² − 4AC = 0, the equation is Parabolic.

(c) Rank Correlation

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Trigonometry and Pre-Calculus Problem Solving Techniques

Posted by on May 9, 2026 in Mathematics | 0 comments

Trigonometry and Triangle Calculations

1) Find Tangent Theta: Given sine theta and its quadrant, write sine as a fraction (opposite/hypotenuse). Find the adjacent side using the Pythagorean Theorem, adjust the sign based on the quadrant, and calculate tangent as opposite/adjacent.

2) Solve Triangle (Law of Sines): Use the formula: \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.

3) Solve Triangle: Apply the same Law of Sines method as described above.

15) SOH CAH TOA: Use basic trigonometric ratios

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Operations Management Formulas and Key Definitions

Posted by on Apr 28, 2026 in Mathematics | 0 comments

Waiting Line Management

Definitions and Formulas

  • Arrival rate (λ): Average number of customers arriving per unit time.
    λ = 1 / E(A); where E(A) is the average interarrival time.
  • Service rate (μ): Average number of customers served per unit time per server.
    μ = 1 / E(S); where E(S) is the average service time.
  • Utilization (ρ): Fraction of system capacity being used. This value must be less than 1.
    ρ = λ / (cμ); where c is the number of servers.
  • Coefficient of variation (CV): Measures variability.
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Financial Accounting and Reporting Principles

Posted by on Apr 19, 2026 in Mathematics | 0 comments

Financial Accounting Principles

  1. Declaration of cash dividends increases total liabilities. ANSWER: True
  2. Payment of cash dividends decreases total assets and total equity. ANSWER: False
  3. The cumulative effect of the declaration and payment of a cash dividend will decrease total assets and shareholders’ equity on a company’s financial statements. ANSWER: True
  4. Short-term debt which is expected to be refinanced might not be classified as a current liability. ANSWER: True
  5. Accumulated depreciation is a contra-
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All gust lines in the V-n graph originate from a point where the

Posted by on Apr 15, 2026 in Mathematics | 0 comments

  1. Fractions
    Add/subtract: make the bottom number the same first
    Multiply: top × top, bottom × bottom
    Divide: keep, change, flip

Example:
1/2 + 1/4 = 2/4 + 1/4 = 3/4
2/3 × 4/5 = 8/15
2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6

  1. Sig fig and decimal places
    Decimal places: count digits after the decimal point
    Significant figures: start at first non-zero digit
    If next digit is 5 or more, round up

Example:
3.456 to 2 decimal places = 3.46
0.00456 to 2 sig fig = 0.0046

  1. Factorization
    Common factor: take out the biggest factor
    Quadratic:
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